AI Grammar Clean Up

AI Grammar Clean Up — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Memory color effect

The memory color effect is the phenomenon that the canonical hue of a type of object acquired through experience (e.g. the sky, a leaf, or a strawberry) can directly modulate the appearance of the actual colors of objects. Human observers acquire memory colors through their experiences with instances of that type. For example, most human observers know that an apple typically has a reddish hue; this knowledge about the canonical color which is represented in memory constitutes a memory color. As an example of the effect, normal human trichromats, when presented with a gray banana, often perceive the gray banana as being yellow - the banana's memory color. In light of this, subjects typically adjust the color of the banana towards the color blue - the opponent color of yellow - when asked to adjust its surface to gray to cancel the subtle activation of banana's memory color. Subsequent empirical studies have also shown the memory color effect on man-made objects (e.g. smurfs, German mailboxes), the effect being especially pronounced for blue and yellow objects. To explain this, researchers have argued that because natural daylight shifts from short wavelengths of light (i.e., bluish hues) towards light of longer wavelengths (i.e., yellowish-orange hues) during the day, the memory colors for blue and yellow objects are recruited by the visual system to a higher degree to compensate for this fluctuation in illumination, thereby providing a stronger memory color effect. == Form identification == Memory color plays a role when detecting an object. In a study where participants were given objects, such as an apple, with two alternate forms for each, a crooked apple and a circular apple, researchers changed the colors of the alternate forms and asked if they could identify them. Most of the participants answered "unsure," suggesting that we use memory color when identifying an object. The research redefined memory color as a phenomenon when "a form's identity affects the phenomenal hue of that form." == Color effect on memorization == Memory color effect can be derived from the human instinct to memorize objects better. Comparing the effect of recognizing gray-scaled images and colored images, results showed that people were able to recall colored images 5% higher compared to gray-scaled images. An important factor was that higher level of contrast between the object and background color influences memory. In a specific study related to this, participants reported that colors were 5% to 10% easier to recognize compared to black and white. == Color constancy and memory color effect == Color constancy is the phenomenon where a surface to appear to be of the same color under a wide rage of illumination. A study tested two hypotheses with regards to color memory; the photoreceptor hypothesis and the surface reflectance hypothesis. The test color was surround either by various color patches forming a complex pattern or a uniform “grey” field at the same chromaticity as that of the illuminant. The test color was presented on a dark background for the control group. It was observed that complex surround results where in line with the surface-reflectance hypothesis and not the photoreceptor hypothesis, showing that the accuracy and precision of color memory are fundamentals to understanding the phenomenon of color constancy. == Significance to the evolution of trichromacy == While objects that possess canonical hues make up a small percentage of the objects which populate humans’ visual experience, the human visual system evolved in an environment populated with objects that possess canonical hues. This suggests that the memory color effect is related to the emergence of trichromacy because it has been argued that trichromacy evolved to optimize the ability to detect ripe fruits—objects that appear in canonical hues. == In perception research == In perception research, the memory color effect is cited as evidence for the opponent color theory, which states that four basic colors can be paired with its opponent color: red—green, blue—yellow. This explains why participants adjust the ripe banana color to a blueish tone to make its memory color yellow as gray. Researchers have also found empirical evidence that suggests memory color is recruited by the visual system to achieve color constancy. For example, participants had a lower percentage of color constancy when looking at a color incongruent scene, such as a purple banana, compared to a color diagnostical scene, a yellow banana. This suggests that color constancy is influenced by the color of objects that we are familiar with, which the memory color effect takes part.
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Media contacts database

In public relations (PR) and marketing, a media contacts database is a resource which catalogs the names, contact information, and other details about people who work in various media professions. These include journalists, reporters, editors, publishers, contributors, freelance journalists, opinion writers, social media personalities/ influencers, TV show anchors, radio show hosts, DJs, and others. A media contacts database usually contains the following information: Full name of the media contact, The publication or channel they work for Designations (past and present) Topics they cover, or their beat Contact information found in public domains Online presence like blogs and other social networking sites Education Information == Overview == A media contacts database is a public relations tool that is maintained and used by PR professionals to pitch stories on a particular topic, product, or company to a specific group of journalists. These journalists would then write or speak about the particular topic in a relevant issue or episode of their shows. A media contacts database allows a PR professional to gain easy access to hundreds of journalists within a short span of time. Media contacts database are created and sold by many media research companies that offer such PR software for professionals.
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Content management

Content management (CM) are a set of processes and technologies that support the collection, managing, and publishing of information in any form or medium. When stored and accessed via computers, this information may be more specifically referred to as digital content, or simply as content. Digital content may take the form of text (such as electronic documents), images, multimedia files (such as audio or video files), or any other file type that follows a content lifecycle requiring management. The process of content development and management is complex enough that various commercial software vendors (large and small), such as Interwoven and Microsoft, offer content management software to control and automate significant aspects of the content lifecycle. == Process == Content management practices and goals vary by mission and by organizational governance structure. News organizations, e-commerce websites, and educational institutions all use content management, but in different ways. This leads to differences in terminology and in the names and number of steps in the process. For example, some digital content is created by one or more authors. Over time that content may be edited. One or more individuals may provide some editorial oversight, approving the content for publication. Publishing may take many forms: it may be the act of "pushing" content out to others, or simply granting digital access rights to certain content to one or more individuals. Later that content may be superseded by another version of the content and thus retired or removed from use (as when this wiki page is modified). Content management is an inherently collaborative process. It often consists of the following basic roles and responsibilities: Creator – responsible for creating and editing content. Editor – responsible for tuning the content message and the style of delivery, including translation and localization. Publisher – responsible for releasing the content for use. Administrator – responsible for managing access permissions to folders, collections and files, usually accomplished by assigning access rights to user groups or roles. Admins may also assist and support users in various ways. Consumer, viewer or guest – the person who reads or otherwise consumes the content after it is published or shared. A critical aspect of content management is the ability to manage versions of content as it evolves (see also version control). Authors and editors often need to restore older versions of edited products due to a process failure or an undesirable series of edits. Time-sensitive content may also require updates as the subject matter evolves over time. Another equally important aspect of content management involves the creation, maintenance, and application of review standards. Each member of the content creation and review process has a unique role and set of responsibilities in the development or publication of the content. Each review team member requires clear and concise review standards. These must be maintained on an ongoing basis to ensure the long-term consistency and health of the knowledge base. A content management system is a set of automated processes that may support the following features: Import and creation of documents and multimedia material Identification of all key users and their roles The ability to assign roles and responsibilities to different instances of content categories or types Definition of workflow tasks often coupled with messaging so that content managers are alerted to changes in content The ability to track and manage multiple versions of a single instance of content The ability to publish the content to a repository to support access The ability to personalize content based on a set of rules Increasingly, the repository is an inherent part of the system, and incorporates enterprise search and retrieval. Content management systems take the following forms: Web content management system—software for web site management (often what content management implicitly means) Output of a newspaper editorial staff organization Workflow for article publication Document management systems Knowledge management software Single source content management system—content stored in chunks within a relational database Variant management system—where personnel tag source content (usually text and graphics) to represent variants stored as single source "master" content modules, resolved to the desired variant at publication (for example: automobile owners manual content for 12 model years stored as single master content files and "called" by model year as needed)—often used in concert with database chunk storage (see above) for large content objects == Governance structures == Content management expert Marc Feldman defines three primary content management governance structures: localized, centralized, and federated—each having its unique strengths and weaknesses. === Localized governance === By putting control in the hands of those closest to the content, the context experts, localized governance models empower and unleash creativity. These benefits come, however, at the cost of a partial-to-total loss of managerial control and oversight. === Centralized governance === When the levers of control are strongly centralized, content management systems are capable of delivering an exceptionally clear and unified brand message. Moreover, centralized content management governance structures allow for a large number of cost-savings opportunities in large enterprises, realized, for example, through (1) the avoidance of duplicated efforts in creating, editing, formatting, repurposing and archiving content; (2) process management and the streamlining of all content related labor; and/or (3) an orderly deployment or updating of the content management system. === Federated governance === Federated governance models potentially realize the benefits of both localized and centralized control while avoiding the weaknesses of both. While content management software systems are inherently structured to enable federated governance models, realizing these benefits can be difficult because it requires, for example, negotiating the boundaries of control with local managers and content creators. In the case of larger enterprises, in particular, the failure to fully implement or realize a federated governance structure equates to a failure to realize the full return on investment and cost savings that content management systems enable. == Implementation == Content management implementations must be able to manage content distributions and digital rights in content life cycle. Content management systems are usually involved with digital rights management in order to control user access and digital rights. In this step, the read-only structures of digital rights management systems force some limitations on content management, as they do not allow authors to change protected content in their life cycle. Creating new content using managed (protected) content is also an issue that gets protected contents out of management controlling systems. A few content management implementations cover all these issues.
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Content-oriented workflow models

In data management, a content-oriented workflow model seeks to articulate workflow progression by the presence of content units (like data-records/objects/documents). Most content-oriented workflow approaches provide a life-cycle model for content units, such that workflow progression can be qualified by conditions on the state of the units. Most approaches are research and work in progress and the content models and life-cycle models are more or less formalized. The term content-oriented workflows is an umbrella term for several scientific workflow approaches, namely "data-driven", "resource-driven", "artifact-centric", "object-aware", and "document-oriented". Thus, the meaning of "content" ranges from simple data attributes to self-contained documents; the term "content-oriented workflows" appeared at first in as an umbrella term. Such a general term, independent from a specific approach, is necessary to contrast the content-oriented modelling principle with traditional activity-oriented workflow models (like Petri nets or BPMN) where a workflow is driven by a control flow and where the content production perspective is neglected or even missing. The term "content" was chosen to subsume the different levels in granularity of the content units in the respective workflow models; it was also chosen to make associations with content management. Both terms "artifact-centric" and "data-driven" would also be good candidates for an umbrella term, but each is closely related to a specific approach of a single working group. The "artifact-centric" group itself (i.e. IBM Research) has generalized the characteristics of their approach and has used "information-centric" as an umbrella term in. Yet, the term information is too unspecific in the context of computer science, thus, "content-orientated workflows" is considered as good compromise. == Workflow Model Approaches == === Data-driven === The data-driven process structures provides a sophisticated workflow model being specialized on hierarchical write-and-review-processes. The approach provides interleaved synchronization of sub-processes and extends activity diagrams. Unfortunately, the COREPRO prototype implementation is not publicly available. Research on the project had been ceased. The general idea has been continued by Reichert in form of the #Object-aware approach. Synonyms data-driven process structures / data-driven modeling and coordination Protagonists Dr. Dominic Müller (University of Twente), Joachim Herbst (DaimlerChrysler Research), and Manfred Reichert (at this time Assoc. Prof. at Univ. of Twente, currently Prof. at Ulm Univ.) Organization(s) University of Twente, DaimlerChrysler Period 2005 - 2007 Selected publications Implementation COREPRO === Resource-driven === The resource-driven workflow system is an early approach that considered workflows from a content-oriented perspective and emphasizes on the missing support for plain document-driven processes by traditional activity-oriented workflow engines. The resource-driven approach demonstrated the application of database triggers for handling workflow events. Still the system implementation is centralized and the workflow schema is statically defined. The project appeared in 2005 but many aspects are considered future work by the authors. Research did not continue on the project. Wang completed his PhD thesis in 2009, yet, his thesis does not mention the resource-driven approach to workflow modelling but is about discrete event simulation. Synonyms Resource-based Workflows / Document-Driven Workflow Systems Protagonists Jianrui Wang and Prof. Akhil Kumar Organization Pennsylvania State University Period 2005 - today Selected publications Implementation N/A === Artifact-centric === The artifact-centric approach provides a framework for content-oriented workflows. In this model, the enterprise application landscape includes distributed business services, while the workflow engine is centralized. Process enactment is integrated with database management system infrastructure, and the project is funded by IBM. Synonyms artifact-centric business process models / artifact-based business process (ACP) / artifact-centric workflows Protagonists Richard Hull and Dr. Kamal Bhattacharya as well as Cagdas E. Gerede and Jianwen Su Organization IBM (T.J. Watson Research Center, NY) Period 2007 - today Selected publications Implementation ArtiFact === Object-aware === The object-aware approach manages a set of object types and generates forms for creating object instances. The form completion flow is controlled by transitions between object configurations each describing a progressing set of mandatory attributes. Each object configuration is named by an object state. The data production flow is user-shifting and it is discrete by defining a sequence of object states. The discussion is currently limited to a centralized system, without any workflows across different organizations. However, the approach is of great relevance to many domains like concurrent engineering. Finally, the object-aware approach and its PHILharmonicFlows system are going to provide general-purpose workflow systems for generic enactment of data production processes. Synonyms object-aware process management / datenorientiertes Prozess-Management-System Protagonists Vera Künzle and Prof. Manfred Reichert Organization Ulm University Period 2009 - today Selected publications Implementation PHILharmonicFlows === Distributed Document-oriented === Distributed document-oriented process management (dDPM) enables distributed case handling in heterogeneous system environments and it is based on document-oriented integration. The workflow model reflects the paper-based working practice in inter-institutional healthcare scenarios. It targets distributed knowledge-driven ad hoc workflows, wherein distributed information systems are required to coordinate work with initially unknown sets of actors and activities. The distributed workflow engine supports process planning & process history as well as participant management and process template creation with import/export. The workflow engine embeds a functional fusion of 1) group-based instant messaging 2) with a shared work list editor 3) with version control. The software implementation of dDPM is α-Flow which is available as open source. dDPM and α-Flow provide a content-oriented approach to schema-less workflows. The complete distributed case handling application is provided in form of a single active Document ("α-Doc"). The α-Doc is a case file (as information carrier) with an embedded workflow engine (in form of active properties). Inviting process participants is equivalent to providing them with a copy of an α-Doc, copying it like an ordinary desktop file. All α-Docs that belong to the same case can synchronize each other, based on the participant management, electronic postboxes, store-and-forward messaging, and an offline-capable synchronization protocol. Synonyms distributed document-oriented process management (dDPM), distributed case handling via active documents Protagonists Christoph P. Neumann and Prof. Richard Lenz Organization Friedrich-Alexander-Universität Erlangen-Nürnberg Period 2009 - 2012 Selected Publications and a PhD thesis Implementation α-Flow (open source) == Related Concepts == === Content Management === The bandwidth of Content management systems (CMS) reaches from Web content management systems (WCMS) and Document management system (DMS) to Enterprise Content Management (ECM). Mature DMS products support document production workflows in a basic form, primarily focusing on review cycle workflows concerning a single document. === Groupware and Computer-Supported Cooperative Work === Groupware focuses on messaging (like E-Mail, Chat, and Instant Messaging), shared calendars (e.g. Lotus Notes, Microsoft Outlook with Exchange Server), and conferencing (e.g. Skype). Groupware overlaps with Computer-supported cooperative work (CSCW), that originated from shared multimedia editors (for live drawing/sketching) and synchronous multi-user applications like desktop sharing. The extensive conceptual claim of CSWC must be put into perspective by its actual solution scope, that is available as the CSCW Matrix. === Case Handling === The case handling paradigm stems from Prof. van der Aalst and gained momentum in 2005. The core features are: (a) provide all information available, i.e. present the case as a whole rather than showing bits and pieces, (b) decide about activities on the basis of the information available rather than the activities already executed, (c) separate work distribution from authorization and allow for additional types of roles, not just the execute role, and (d) allow workers to view and add/modify data before or after the corresponding activities have been executed. In healthcare, the flow of a patient between healthcare professionals is considered as a workflow - with activities that inc
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Noom

Noom is an American privately held digital health company that provides weight management and behavioral health services through a subscription-based mobile application. Founded in 2008, the company combines behavior change psychology with access to weight loss medications and dietary supplements. The platform incorporates elements of cognitive behavioral therapy (CBT) and goal-setting strategies, and its programs are designed to support users in developing healthier habits. In addition to its weight management services, Noom has expanded to offer products related to stress management and general wellness. Noom has received both praise and criticism. Supporters cite its focus on mental and behavioral aspects of health, while critics have raised concerns about the accuracy of its calorie goals, the use of algorithmically determined weight loss targets, and questions about the qualifications of some of its coaching staff. == History == Noom was founded in 2008 by friends Artem Petakov and Saeju Jeong. The company's mobile app officially launched in 2016. In 2025, Noom relocated its headquarters from New York City to Princeton, New Jersey. Petakov, a former software engineer at Google, currently leads Noom Ventures, while Jeong serves as Noom's Chairman. In 2023, Geoff Cook was appointed CEO of Noom. In 2019, Noom partnered with Novo Nordisk to offer patients prescribed the diabetes medication Saxenda one year of free access to the Noom platform. In 2020, Noom reported $400 million in revenue. As of April 2021, the company stated it employed approximately 3,000 people, including 2,700 coaches. == Services == === Noom App === The Noom app is the primary platform through which users engage with the company's services. Upon creating an account, users are prompted to provide physical information such as weight, height, and age, along with experiential data including lifestyle habits, personal goals, and perceived obstacles. Users log their meals and physical activity, and in return, the app delivers feedback through multiple channels: algorithmically generated insights, guidance from a human coach, peer interaction, educational articles, and interactive quizzes. The app has been reviewed by a range of media outlets, including newspapers such as the Chicago Tribune and USA Today; health information sources such as WebMD; and lifestyle magazines including Good Housekeeping. === Other services === In 2024, Noom launched Noom Vibe, a mobile application that encourages users to develop healthy habits by awarding "vibes"—a form of points—for activities such as walking or meeting step goals. That same year, Noom introduced a 3D body scanning feature within its app, designed to help users monitor physical changes and prevent muscle atrophy during weight loss. Also in 2024, Noom began offering a compounded GLP-1 medication as part of its weight management program. The formulation includes the same active ingredient found in the anti-obesity medications Wegovy and Ozempic. == Research == In 2016, a study published in Scientific Reports analyzed data from approximately 36,000 users of the Noom app, of whom 78% were female and 22% male. The data were collected between October 2012 and April 2014. To be included in the analysis, users had to log their weight at least twice per month over a period of six consecutive months. The study found that 78% of participants self-reported weight loss while using the app. The median duration of weight reporting was 267 days (approximately nine months). The frequency of data logging was positively correlated with weight loss. Additionally, male users had a higher average starting BMI and reported greater average weight loss compared to female users. In 2017, the Centers for Disease Control and Prevention (CDC) recognized Noom as a certified diabetes prevention program, making it the first mobile health application to receive such designation. == Criticisms == === Health programs === Noom has been criticized for promoting elements of diet culture in its advertising campaigns. The app has also faced criticism for setting calorie goals that some users and experts have deemed inappropriately low, and for employing coaches who may lack formal qualifications as registered dietitians. Coaching has been described as relying heavily on canned responses. Upon sign-up, users are prompted to complete a questionnaire consisting of over 50 questions, which is used to generate a personalized program. In 2021, the UK-based organization Privacy International alleged that Noom, along with other diet platforms, used such lengthy surveys to attract users but did not always tailor the resulting programs to the collected data. The organization claimed that many users received the same or highly similar programs regardless of their answers. It also raised concerns about the handling of potentially sensitive health data, alleging a lack of transparency regarding the sharing of such data with third parties, including Facebook, potentially in violation of the European General Data Protection Regulation (GDPR). In a follow-up investigation in 2023, Privacy International reported that Noom had made "significant positive changes" to its data handling practices. However, the organization noted that data was still being shared with Facebook and concluded that "there is still room for improvement." === Billing issues lawsuit === In August 2020, the Better Business Bureau (BBB) issued a warning to consumers regarding Noom's subscription practices. The BBB reported that numerous customers had filed complaints about difficulties canceling their subscriptions after the free trial period, as well as challenges in contacting the company to request refunds. In February 2022, Noom agreed to a $62 million settlement in a class-action lawsuit that alleged the company had used deceptive billing practices related to automatic subscription renewals. Qualifying claimants received approximately $167 each. During the case, a former senior software engineer at Noom testified that the cancellation process was intentionally designed to be difficult, with the goal of generating revenue from customers who failed to cancel in time. In response, Noom stated that it had taken steps to improve transparency around its pricing and policies, including the implementation of self-service cancellation tools.
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Knapsack problem

The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision-makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating back to 1897. The subset sum problem is a special case of the decision and 0-1 problems where for each kind of item, the weight equals the value: w i = v i {\displaystyle w_{i}=v_{i}} . In the field of cryptography, the term knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. == Applications == Knapsack problems appear in real-world decision-making processes in a wide variety of fields, such as finding the least wasteful way to cut raw materials, selection of investments and portfolios, selection of assets for asset-backed securitization, and generating keys for the Merkle–Hellman and other knapsack cryptosystems. One early application of knapsack algorithms was in the construction and scoring of tests in which the test-takers have a choice as to which questions they answer. For small examples, it is a fairly simple process to provide the test-takers with such a choice. For example, if an exam contains 12 questions each worth 10 points, the test-taker need only answer 10 questions to achieve a maximum possible score of 100 points. However, on tests with a heterogeneous distribution of point values, it is more difficult to provide choices. Feuerman and Weiss proposed a system in which students are given a heterogeneous test with a total of 125 possible points. The students are asked to answer all of the questions to the best of their abilities. Of the possible subsets of problems whose total point values add up to 100, a knapsack algorithm would determine which subset gives each student the highest possible score. A 1999 study of the Stony Brook University Algorithm Repository showed that, out of 75 algorithmic problems related to the field of combinatorial algorithms and algorithm engineering, the knapsack problem was the 19th most popular and the third most needed after suffix trees and the bin packing problem. == Definition == The most common problem being solved is the 0-1 knapsack problem, which restricts the number x i {\displaystyle x_{i}} of copies of each kind of item to zero or one. Given a set of n {\displaystyle n} items numbered from 1 up to n {\displaystyle n} , each with a weight w i {\displaystyle w_{i}} and a value v i {\displaystyle v_{i}} , along with a maximum weight capacity W {\displaystyle W} , maximize ∑ i = 1 n v i x i {\displaystyle \sum _{i=1}^{n}v_{i}x_{i}} subject to ∑ i = 1 n w i x i ≤ W {\displaystyle \sum _{i=1}^{n}w_{i}x_{i}\leq W} and x i ∈ { 0 , 1 } {\displaystyle x_{i}\in \{0,1\}} . Here x i {\displaystyle x_{i}} represents the number of instances of item i {\displaystyle i} to include in the knapsack. Informally, the problem is to maximize the sum of the values of the items in the knapsack so that the sum of the weights is less than or equal to the knapsack's capacity. The bounded knapsack problem (BKP) removes the restriction that there is only one of each item, but restricts the number x i {\displaystyle x_{i}} of copies of each kind of item to a maximum non-negative integer value c {\displaystyle c} : maximize ∑ i = 1 n v i x i {\displaystyle \sum _{i=1}^{n}v_{i}x_{i}} subject to ∑ i = 1 n w i x i ≤ W {\displaystyle \sum _{i=1}^{n}w_{i}x_{i}\leq W} and x i ∈ { 0 , 1 , 2 , … , c } . {\displaystyle x_{i}\in \{0,1,2,\dots ,c\}.} The unbounded knapsack problem (UKP) places no upper bound on the number of copies of each kind of item and can be formulated as above except that the only restriction on x i {\displaystyle x_{i}} is that it is a non-negative integer. maximize ∑ i = 1 n v i x i {\displaystyle \sum _{i=1}^{n}v_{i}x_{i}} subject to ∑ i = 1 n w i x i ≤ W {\displaystyle \sum _{i=1}^{n}w_{i}x_{i}\leq W} and x i ∈ N . {\displaystyle x_{i}\in \mathbb {N} .} One example of the unbounded knapsack problem is given using the figure shown at the beginning of this article and the text "if any number of each book is available" in the caption of that figure. == Computational complexity == The knapsack problem is interesting from the perspective of computer science for many reasons: The decision problem form of the knapsack problem (Can a value of at least V be achieved without exceeding the weight W?) is NP-complete, thus there is no known algorithm that is both correct and fast (polynomial-time) in all cases. There is no known polynomial algorithm which can tell, given a solution, whether it is optimal (which would mean that there is no solution with a larger V). This problem is co-NP-complete. There is a pseudo-polynomial time algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine, described below. Many cases that arise in practice, and "random instances" from some distributions, can nonetheless be solved exactly. There is a link between the "decision" and "optimization" problems in that if there exists a polynomial algorithm that solves the "decision" problem, then one can find the maximum value for the optimization problem in polynomial time by applying this algorithm iteratively while increasing the value of k. On the other hand, if an algorithm finds the optimal value of the optimization problem in polynomial time, then the decision problem can be solved in polynomial time by comparing the value of the solution output by this algorithm with the value of k. Thus, both versions of the problem are of similar difficulty. One theme in research literature is to identify what the "hard" instances of the knapsack problem look like, or viewed another way, to identify what properties of instances in practice might make them more amenable than their worst-case NP-complete behaviour suggests. The goal in finding these "hard" instances is for their use in public-key cryptography systems, such as the Merkle–Hellman knapsack cryptosystem. More generally, better understanding of the structure of the space of instances of an optimization problem helps to advance the study of the particular problem and can improve algorithm selection. Furthermore, notable is the fact that the hardness of the knapsack problem depends on the form of the input. If the weights and profits are given as integers, it is weakly NP-complete, while it is strongly NP-complete if the weights and profits are given as rational numbers. However, in the case of rational weights and profits it still admits a fully polynomial-time approximation scheme. === Unit-cost models === The NP-hardness of the Knapsack problem relates to computational models in which the size of integers matters (such as the Turing machine). In contrast, decision trees count each decision as a single step. Dobkin and Lipton show an 1 2 n 2 {\displaystyle {1 \over 2}n^{2}} lower bound on linear decision trees for the knapsack problem, that is, trees where decision nodes test the sign of affine functions. This was generalized to algebraic decision trees by Steele and Yao. If the elements in the problem are real numbers or rationals, the decision-tree lower bound extends to the real random-access machine model with an instruction set that includes addition, subtraction and multiplication of real numbers, as well as comparison and either division or remaindering ("floor"). This model covers more algorithms than the algebraic decision-tree model, as it encompasses algorithms that use indexing into tables. However, in this model all program steps are counted, not just decisions. An upper bound for a decision-tree model was given by Meyer auf der Heide who showed that for every n there exists an O(n4)-deep linear decision tree that solves the subset-sum problem with n items. Note that this does not imply any upper bound for an algorithm that should solve the problem for any given n. == Solving == Several algorithms are available to solve knapsack problems, based on the dynamic programming approach, the branch and bound approach or hybridizations of both approaches. === Dynamic programming in-advance algorithm === The unbounded knapsack problem (UKP) places no restriction on the number of copies of each kind of item. Besides, here we assume that x i > 0 {\displaystyle x_{i}>0} m [ w ′ ] = max ( ∑ i = 1 n v i x i ) {\displaystyle m[w']=\max \left(\sum _{i=1}^{n}v_{i}x_{i}\right)} subject to ∑
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Social commerce

Social commerce is a subset of electronic commerce that involves social media and online media that supports social interaction, and user contributions to assist online buying and selling of products and services. More succinctly, social commerce is the use of social network(s), and user-generated content in the context of e-commerce transactions. The term social commerce was introduced by Yahoo! in November 2005 which describes a set of online collaborative shopping tools such as shared pick lists, user ratings and other user-generated content of online product information and advice. The concept of social commerce was developed by David Beisel to denote user-generated advertorial content on e-commerce sites, and by Steve Rubel to include collaborative e-commerce tools that enable shoppers "to get advice from trusted individuals, find goods and services and then purchase them". The social networks that spread this advice have been found to increase the customer's trust in one retailer over another. Social commerce may assist companies in achieving the following purposes: Firstly, social commerce helps companies engage customers with their brands according to the customers' social behaviors. Secondly, it provides an incentive for customers to return to their website. Thirdly, it provides customers with a platform to talk about their brand on their website. Fourthly, it provides all the information customers need to research, compare, and ultimately choose you over your competitor, thus purchasing from you and not others. In these days, the range of social commerce has been expanded to include social media tools and content used in the context of e-commerce, especially in the fashion industry. Examples of social commerce include customer ratings and reviews, user recommendations and referrals, social shopping tools (sharing the act of shopping online), forums and communities, social media optimization, social applications and social advertising. Technologies such as augmented reality have also been integrated with social commerce, allowing shoppers to visualize apparel items on themselves and solicit feedback through social media tools. Some academics have sought to distinguish "social commerce" from "social shopping", with the former being referred to as collaborative networks of online vendors; the latter, the collaborative activity of online shoppers. == Timeline == 2005: The term "social commerce" was first introduced on Yahoo! in 2005. 2021: The Global Web Index associated one's use of social media to his/her eagerness to buy. Social media with its entertaining and inspirational content can increase a product's profitability. This explains why Instagram expanded its Checkout feature to similar content like IG Stories, IGTV, and Reels. == Elements == The attraction and effectiveness of Social Commerce can be understood in terms of Robert Cialdini's Principles of InfluenceInfluence: Science and Practice": Reciprocity – When a company gives a person something for free, that person will feel the need to return the favor, whether by buying again or giving good recommendations for the company. Community – When people find an individual or a group that shares the same values, likes, beliefs, etc., they find community. People are more committed to a community that they feel accepted within. When this commitment happens, they tend to follow the same trends as a group and when one member introduces a new idea or product, it is accepted more readily based on the previous trust that has been established. It would be beneficial for companies to develop partnerships with social media sites to engage social communities with their products. Social proof – To receive positive feedback, a company needs to be willing to accept social feedback and to show proof that other people are buying, and like, the same things that I like. This can be seen in a lot of online companies such as eBay and Amazon, that allow public feedback of products and when a purchase is made, they immediately generate a list showing purchases that other people have made in relation to my recent purchase. It is beneficial to encourage open recommendation and feedback. This creates trust for you as a seller. 55% of buyers turn to social media when they're looking for information. Authority – Many people need proof that a product is of good quality. This proof can be based on the recommendations of others who have bought the same product. If there are many user reviews about a product, then a consumer will be more willing to trust their own decision to buy this item. Liking – People trust based on the recommendations of others. If there are a lot of "likes" of a particular product, then the consumer will feel more confident and justified in making this purchase. Scarcity – As part of supply and demand, a greater value is assigned to products that are regarded as either being in high demand or are seen as being in a shortage. Therefore, if a person is convinced that they are purchasing something that is unique, special, or not easy to acquire, they will have more of a willingness to make a purchase. If there is trust established from the seller, they will want to buy these items immediately. This can be seen in the cases of Zara and Apple Inc. who create demand for their products by convincing the public that there is a possibility of missing out on being able to purchase them. == Types == === Onsite === Onsite social commerce refers to retailers including social sharing and other social functionality on their website. Some notable examples include Zazzle which enables users to share their purchases, Macy's which allows users to create a poll to find the right product, and Fab.com which shows a live feed of what other shoppers are buying. Onsite user reviews are also considered a part of social commerce. This approach has been successful in improving customer engagement, conversion and word-of-mouth branding according to several industry sources. === Offsite === Offsite social commerce includes activities that happen outside of the retailers' website. This may include posting products on social networks such as Facebook, X, and TikTok. It may also include advertising on shopping forums such as SlickDeals, Red Flag Deals, and LatestDeals.co.uk. == Measurements == Social commerce can be measured by any of the principle ways to measure social media. Return on Investment: measures the effect or action of social media on sales. Reputation: indices measure the influence of social media investment in terms of changes to online reputation – made up of the volume and valence of social media mentions. Reach: metrics use traditional media advertising metrics to measure the exposure rates and levels of an audience with social media. == Business applications == This category is based on individuals' shopping, selling, recommending behaviors. Social network-driven sales (Soldsie) – Facebook commerce and Twitter commerce belong to this part. Sales take place on established social network sites. Peer-to-peer sales platforms (eBay, Etsy, Amazon) – In these websites, users can directly communicate and sell products to other users. Group buying (Groupon, LivingSocial) – Users can buy products or services at a lower price when enough users agree to make this purchase. Peer recommendations and reviews (Amazon, Yelp, Bazaarvoice) – Users can see recommendations and reviews from other users. User-curated shopping (The Fancy, Lyst) – Users create and share lists of products and services for others to shop from. Participatory commerce (Betabrand, Threadless, Kickstarter) – Users can get involved in the production process. Social shopping (Squadded) – Allowing e-commerce to provide their users live chat sessions and shared shopping lists so they can communicate with their friends or other shoppers for advice. == Business examples == Here are some notable business examples of Social Commerce: Betabrand: an online brand using participatory design to release new, community-created ideas every week. Cafepress: an online retailer of stock and user-customized on demand products. Etsy: an e-commerce website focused on handmade or vintage items and supplies, as well as unique factory-manufactured items under Etsy's new guidelines. Eventbrite: an online ticketing service that allows event organizers to plan, set up ticket sales and promote events (event management) and publish them across Facebook, Twitter and other social-networking tools directly from the site's interface. Groupon: a deal-of-the-day website that features discounted gift certificates usable at local or national companies. Houzz: a web site and online community about architecture, interior design and decorating, landscape design and home improvement. LivingSocial: an online marketplace that allows clients to buy and share things to do in their city. Lockerz: an international social commerce website based in Seattle, Washington. OpenSky: is a r
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Cryptographic nonce

In cryptography, a nonce is an arbitrary number that can be used just once in a cryptographic communication. It is often a random or pseudo-random number issued in an authentication protocol to ensure that each communication session is unique, and therefore that old communications cannot be reused in replay attacks. Nonces can also be useful as initialization vectors and in cryptographic hash functions. == Definition == A nonce is an arbitrary number used only once in a cryptographic communication, in the spirit of a nonce word. They are often random or pseudo-random numbers. Many nonces also include a timestamp to ensure exact timeliness, though this requires clock synchronisation between organisations. The addition of a client nonce ("cnonce") helps to improve the security in some ways as implemented in digest access authentication. To ensure that a nonce is used only once, it should be time-variant (including a suitably fine-grained timestamp in its value), or generated with enough random bits to ensure an insignificantly low chance of repeating a previously generated value. Some authors define pseudo-randomness (or unpredictability) as a requirement for a nonce. Nonce is a word dating back to Middle English for something only used once or temporarily (often with the construction "for the nonce"). It descends from the construction "then anes" ("the one [purpose]"). A false etymology claiming it to stand for "number used once" or similar is incorrect. == Usage == === Authentication === Authentication protocols may use nonces to ensure that old communications cannot be reused in replay attacks. For instance, nonces are used in HTTP digest access authentication to calculate an MD5 digest of the password. The nonces are different each time the 401 authentication challenge response code is presented, thus making replay attacks virtually impossible. The scenario of ordering products over the Internet can provide an example of the usefulness of nonces in replay attacks. An attacker could take the encrypted information and—without needing to decrypt—could continue to send a particular order to the supplier, thereby ordering products over and over again under the same name and purchase information. The nonce is used to give 'originality' to a given message so that if the company receives any other orders from the same person with the same nonce, it will discard those as invalid orders. A nonce may be used to ensure security for a stream cipher. Where the same key is used for more than one message and then a different nonce is used to ensure that the keystream is different for different messages encrypted with that key; often the message number is used. Secret nonce values are used by the Lamport signature scheme as a signer-side secret which can be selectively revealed for comparison to public hashes for signature creation and verification. === Hashing === Nonces are used in proof-of-work systems to vary the input to a cryptographic hash function so as to obtain a hash for a certain input that fulfils certain arbitrary conditions. In doing so, it becomes far more difficult to create a "desirable" hash than to verify it, shifting the burden of work onto one side of a transaction or system. For example, proof of work, using hash functions, was considered as a means to combat email spam by forcing email senders to find a hash value for the email (which included a timestamp to prevent pre-computation of useful hashes for later use) that had an arbitrary number of leading zeroes, by hashing the same input with a large number of values until a "desirable" hash was obtained. Similarly, the Bitcoin blockchain hashing algorithm can be tuned to an arbitrary difficulty by changing the required minimum/maximum value of the hash so that the number of bitcoins awarded for new blocks does not increase linearly with increased network computation power as new users join. This is likewise achieved by forcing Bitcoin miners to add nonce values to the value being hashed to change the hash algorithm output. As cryptographic hash algorithms cannot easily be predicted based on their inputs, this makes the act of blockchain hashing and the possibility of being awarded bitcoins something of a lottery, where the first "miner" to find a nonce that delivers a desirable hash is awarded bitcoins.
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Unspent transaction output

In cryptocurrencies, an unspent transaction output (UTXO, often capitalized as UTxO) is a distinctive element in a subset of digital currency models. A UTXO represents a certain amount of cryptocurrency that has been authorized by a sender and is available to be spent by a recipient. The utilization of UTXOs in transaction processes is a key feature of many cryptocurrencies, but it primarily characterizes those implementing the UTXO model. UTXOs employ public key cryptography to ascertain and transfer ownership. More specifically, the recipient's public key is formatted into the UTXO, thereby limiting the capability to spend the UTXO to the account that can demonstrate ownership of the corresponding private key. A valid digital signature associated with the public key must be included for the UTXO to be spent. In the UTXO model, each unit of currency is treated as a discrete object. The history of a UTXO is documented only within the blocks where it is transferred. To ascertain the total balance of an account, one must scan each block to find the latest UTXOs linked to that account. While all nodes within a blockchain network must consent to the block history, the blocks relevant to an account's balance are unique to that account. UTXOs constitute a chain of ownership depicted as a series of digital signatures dating back to the coin's inception, regardless of whether the coin was minted via mining, staking, or another procedure determined by the cryptocurrency protocol. The UTXO model was invented for Bitcoin. Cardano uses an extended version of the UTXO model known as EUTXO. == Origins == The conceptual framework of the UTXO model can be traced back to Hal Finney's Reusable Proofs of Work proposal, which itself was based on Adam Back's 1997 Hashcash proposal. Bitcoin, released in 2009, was the first widespread implementation of the UTXO model in practice. == UTXO model vs. account Model == Cryptocurrencies that utilize the UTXO model function differently compared to those using the account model. In the UTXO model, individual units of cryptocurrency, termed as unspent transaction outputs (UTXOs), are transferred between users, analogous to the exchange of physical cash. This model impacts how transactions and ownership are recorded and verified within the blockchain network. The account model preserves a record of each account and its corresponding balance for every block added to the network. This setup enables quicker balance verification without the need to scan historical blocks, but it increases the raw size of each block (though data compression techniques can be utilized to alleviate this). However, both models necessitate the inspection of past blocks to fully authenticate the origin of coins. In the UTXO model, each object is immutable - units of coins cannot be 'edited' in the same way an account balance is modified when a transaction occurs. Rather, the balance is computed from the transaction history dating back to when the coins were first minted. This simplicity enhances security, as a UTXO either exists in its anticipated form or it does not. In contrast, the account model requires meticulous verification of the account's status during transactions, which can lead to oversights if not conducted correctly. In valid blockchain transactions, only unspent outputs (UTXOs) are permissible for funding subsequent transactions. This requirement is critical to prevent double-spending and fraud. Accordingly, inputs in a transaction are removed from the UTXO set, while outputs create new UTXOs that are added to the set. The holders of private keys, such as those with cryptocurrency wallets, can utilize these UTXOs for future transactions.
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SFINKS

Sfinks (Polish for "Sphynx") was also the initial name of the Janusz A. Zajdel Award In cryptography, SFINKS is a stream cypher algorithm developed by An Braeken, Joseph Lano, Nele Mentens, Bart Preneel, and Ingrid Verbauwhede. It includes a message authentication code. It has been submitted to the eSTREAM Project of the eCRYPT network. In 2005, Nicolas T. Courtois noted that, while the cipher is elegant and secure against some simple algebraic attacks, it is vulnerable to more elaborate known attacks.
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Cryptographic High Value Product

Cryptographic High Value Product (CHVP) is a designation used within the information security community to identify assets that have high value, and which may be used to encrypt / decrypt secure communications, but which do not retain or store any classified information. When disconnected from the secure communication network, the CHVP equipment may be handled with a lower level of controls than required for COMSEC equipment.
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Cryptographic nonce

In cryptography, a nonce is an arbitrary number that can be used just once in a cryptographic communication. It is often a random or pseudo-random number issued in an authentication protocol to ensure that each communication session is unique, and therefore that old communications cannot be reused in replay attacks. Nonces can also be useful as initialization vectors and in cryptographic hash functions. == Definition == A nonce is an arbitrary number used only once in a cryptographic communication, in the spirit of a nonce word. They are often random or pseudo-random numbers. Many nonces also include a timestamp to ensure exact timeliness, though this requires clock synchronisation between organisations. The addition of a client nonce ("cnonce") helps to improve the security in some ways as implemented in digest access authentication. To ensure that a nonce is used only once, it should be time-variant (including a suitably fine-grained timestamp in its value), or generated with enough random bits to ensure an insignificantly low chance of repeating a previously generated value. Some authors define pseudo-randomness (or unpredictability) as a requirement for a nonce. Nonce is a word dating back to Middle English for something only used once or temporarily (often with the construction "for the nonce"). It descends from the construction "then anes" ("the one [purpose]"). A false etymology claiming it to stand for "number used once" or similar is incorrect. == Usage == === Authentication === Authentication protocols may use nonces to ensure that old communications cannot be reused in replay attacks. For instance, nonces are used in HTTP digest access authentication to calculate an MD5 digest of the password. The nonces are different each time the 401 authentication challenge response code is presented, thus making replay attacks virtually impossible. The scenario of ordering products over the Internet can provide an example of the usefulness of nonces in replay attacks. An attacker could take the encrypted information and—without needing to decrypt—could continue to send a particular order to the supplier, thereby ordering products over and over again under the same name and purchase information. The nonce is used to give 'originality' to a given message so that if the company receives any other orders from the same person with the same nonce, it will discard those as invalid orders. A nonce may be used to ensure security for a stream cipher. Where the same key is used for more than one message and then a different nonce is used to ensure that the keystream is different for different messages encrypted with that key; often the message number is used. Secret nonce values are used by the Lamport signature scheme as a signer-side secret which can be selectively revealed for comparison to public hashes for signature creation and verification. === Hashing === Nonces are used in proof-of-work systems to vary the input to a cryptographic hash function so as to obtain a hash for a certain input that fulfils certain arbitrary conditions. In doing so, it becomes far more difficult to create a "desirable" hash than to verify it, shifting the burden of work onto one side of a transaction or system. For example, proof of work, using hash functions, was considered as a means to combat email spam by forcing email senders to find a hash value for the email (which included a timestamp to prevent pre-computation of useful hashes for later use) that had an arbitrary number of leading zeroes, by hashing the same input with a large number of values until a "desirable" hash was obtained. Similarly, the Bitcoin blockchain hashing algorithm can be tuned to an arbitrary difficulty by changing the required minimum/maximum value of the hash so that the number of bitcoins awarded for new blocks does not increase linearly with increased network computation power as new users join. This is likewise achieved by forcing Bitcoin miners to add nonce values to the value being hashed to change the hash algorithm output. As cryptographic hash algorithms cannot easily be predicted based on their inputs, this makes the act of blockchain hashing and the possibility of being awarded bitcoins something of a lottery, where the first "miner" to find a nonce that delivers a desirable hash is awarded bitcoins.
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Stencil buffer

A stencil buffer is an extra data buffer, in addition to the color buffer and Z-buffer, found on modern graphics hardware. The buffer is per pixel and works on integer values, usually with a depth of one byte per pixel. The Z-buffer and stencil buffer often share the same area in the RAM of the graphics hardware. In the simplest case, the stencil buffer is used to limit the area of rendering (stenciling). More advanced usage of the stencil buffer makes use of the strong connection between the Z-buffer and the stencil buffer in the rendering pipeline. For example, stencil values can be automatically increased/decreased for every pixel that fails or passes the depth test. The simple combination of depth test and stencil modifiers make a vast number of effects possible (such as stencil shadow volumes, Two-Sided Stencil, compositing, decaling, dissolves, fades, swipes, silhouettes, outline drawing, or highlighting of intersections between complex primitives) though they often require several rendering passes and, therefore, can put a heavy load on the graphics hardware. The most typical application is still to add shadows to 3D applications. It is also used for planar reflections. Other rendering techniques, such as portal rendering, use the stencil buffer in other ways; for example, it can be used to find the area of the screen obscured by a portal and re-render those pixels correctly. The stencil buffer and its modifiers can be accessed in computer graphics by using APIs like OpenGL, Direct3D, Vulkan or Metal. == Architecture == The stencil buffer typically shares the same memory space as the Z-buffer, and typically the ratio is 24 bits for Z-buffer + 8 bits for stencil buffer or, in the past, 15 bits for Z-buffer + 1 bit for stencil buffer. Another variant is 4 + 24, where 28 of the 32 bits are used and 4 ignored. Stencil and Z-buffers are part of the frame buffer, coupled to the color buffer. The first chip available to a wider market was 3Dlabs' Permedia II, which supported a one-bit stencil buffer. The bits allocated to the stencil buffer can be used to represent numerical values in the range [0, 2n-1], and also as a Boolean matrix (n is the number of allocated bits), each of which may be used to control the particular part of the scene. Any combination of these two ways of using the available memory is also possible. == Stencil test == Stencil test or stenciling is among the operations on the pixels/fragments (Per-pixel operations), located after the alpha test, and before the depth test. The stencil test ensures undesired pixels do not reach the depth test. This saves processing time for the scene. Similarly, the alpha test can prevent corresponding pixels to reach the stencil test. The test itself is carried out over the stencil buffer to some value in it, or altered or used it, and carried out through the so-called stencil function and stencil operations. The stencil function is a function by which the stencil value of a certain pixel is compared to a given reference value. If this comparison is logically true, the stencil test passes. Otherwise not. In doing so, the possible reaction caused by the result of comparing three different state-depth and stencil buffer: Stencil test is not passed Stencil test is passed but not the depth test Both tests are passed (or stencil test is passed, and the depth is not enabled) For each of these cases, different operations can be set over the examined pixel. In the OpenGL stencil functions, the reference value and mask, respectively, define the function glStencilFunc. In Direct3D each of these components is adjusted individually using methods SetRenderState devices currently in control. This method expects two parameters, the first of which is a condition that is set and the other its value. In the order that was used above, these conditions are called D3DRS_STENCILFUNC, D3DRS_STENCILREF, and D3DRS_STENCILMASK. Stencil operations in OpenGL adjust glStencilOp function that expects three values. In Direct3D, again, each state sets a specific method SetRenderState. The three states that can be assigned to surgery are called D3DRS_STENCILFAIL, D3DRENDERSTATE_STENCILZFAIL, and D3DRENDERSTATE_STENCILPASS. == Z-fighting == Due to the lack of precision in the Z-buffer, coplanar polygons that are short-range, or overlapping, can be portrayed as a single plane with a multitude of irregular cross-sections. These sections can vary depending on the camera position and other parameters and are rapidly changing. This is called Z-fighting. There exist multiple solutions to this issue: - Bring the far plane closer to restrict the scene's depth, thus increasing the accuracy of the Z-buffer, or reducing the distance at which objects are visible in the scene. - Increase the number of bits allocated to the Z-buffer, which is possible at the expense of memory for the stencil buffer. - Move polygons farther apart from one another, which restricts the possibilities for the artist to create an elaborate scene. All of these approaches to the problem can only reduce the likelihood that the polygons will experience Z-fighting, and do not guarantee a definitive solution in the general case. A solution that includes the stencil buffer is based on the knowledge of which polygon should be in front of the others. The silhouette of the front polygon is drawn into the stencil buffer. After that, the rest of the scene can be rendered only where the silhouette is negative, and so will not clash with the front polygon. == Shadow volume == Shadow volume is a technique used in 3D computer graphics to add shadows to a rendered scene. They were first proposed by Frank Crow in 1977 as the geometry describing the 3D shape of the region occluded from a light source. A shadow volume divides the virtual world in two: areas that are in shadow and areas that are not. The stencil buffer implementation of shadow volumes is generally considered among the most practical general-purpose real-time shadowing techniques for use on modern 3D graphics hardware. It has been popularised by the video game Doom 3, and a particular variation of the technique used in this game has become known as Carmack's Reverse. == Reflections == Reflection of a scene is drawn as the scene itself transformed and reflected relative to the "mirror" plane, which requires multiple render passes and using of stencil buffer to restrict areas where the current render pass works: Draw the scene excluding mirror areas – for each mirror lock the Z-buffer and color buffer Render visible part of the mirror Depth test is set up so that each pixel is passed to enter the maximum value and always passes for each mirror: Depth test is set so that it passes only if the distance of a pixel is less than the current (default behavior) The matrix transformation is changed to reflect the scene relative to the mirror plane Unlock the Z-buffer and color buffer Draw the scene, but only the part of it that lies between the mirror plane and the camera. In other words, a mirror plane is also a clipping plane Again locks color buffer, depth test is set so that it always passes, reset stencil for the next mirror. == Planar Shadows == While drawing a plane of shadows, there are two dominant problems: The first concerns the problem of deep struggle in case the flat geometry is not awarded on the part covered with the shadow of shadows and outside. See the section that relates to this. Another problem relates to the extent of the shadows outside the area where the plane there. Another problem, which may or may not appear, depending on the technique, the design of more polygons in one part of the shadow, resulting in darker and lighter parts of the same shade. All three problems can be solved geometrically, but because of the possibility that hardware acceleration is directly used, it is a far more elegant implementation using the stencil buffer: 1. Enable lights and the lights 2. Draw a scene without any polygon that should be projected shadows 3. Draw all polygons which should be projected shadows, but without lights. In doing so, the stencil buffer, the pixel of each polygon to be assigned to a specific value for the ground to which they belong. The distance between these values should be at least two, because for each plane to be used two values for two states: in the shadows and bright. 4. Disable any global illumination (to ensure that the next steps will affect only individual selected light) For each plane: For each light: 1. Edit a stencil buffer and only the pixels that carry a specific value for the selected level. Increase the value of all the pixels that are projected objects between the date of a given level and bright. 2. Allow only selected light for him to draw level at which part of her specific value was not changed. == Spatial shadows == Stencil buffer implementation of spatial drawing shadows is any shadow of a geometric body that its volume includes part of the scene that is
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Hybrid argument (cryptography)

In cryptography, the hybrid argument is a proof technique used to show that two distributions are computationally indistinguishable. == History == Hybrid arguments had their origin in a papers by Andrew Yao in 1982 and Shafi Goldwasser and Silvio Micali in 1983. == Formal description == Formally, to show two distributions D1 and D2 are computationally indistinguishable, we can define a sequence of hybrid distributions D1 := H0, H1, ..., Ht =: D2 where t is polynomial in the security parameter n. Define the advantage of any probabilistic efficient (polynomial-bounded time) algorithm A as A d v H i , H i + 1 d i s t ( A ) := | Pr [ x ← $ H i : A ( x ) = 1 ] − Pr [ x ← $ H i + 1 : A ( x ) = 1 ] | , {\displaystyle {\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ):=\left|\Pr[x{\stackrel {\$}{\gets }}H_{i}:\mathbf {A} (x)=1]-\Pr[x{\stackrel {\$}{\gets }}H_{i+1}:\mathbf {A} (x)=1]\right|,} where the dollar symbol ($) denotes that we sample an element from the distribution at random. By triangle inequality, it is clear that for any probabilistic polynomial time algorithm A, A d v D 1 , D 2 d i s t ( A ) ≤ ∑ i = 0 t − 1 A d v H i , H i + 1 d i s t ( A ) . {\displaystyle {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )\leq \sum _{i=0}^{t-1}{\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ).} Thus there must exist some k s.t. 0 ≤ k < t(n) and A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) . {\displaystyle {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n).} Since t is polynomial-bounded, for any such algorithm A, if we can show that it has a fixed negligible advantage function ε(n) between distributions Hi and Hi+1 for every i, so in particular, ϵ ( n ) ≥ A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) , {\displaystyle \epsilon (n)\geq {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n),} then it immediately follows that its advantage to distinguish the distributions D1 = H0 and D2 = Ht must also be negligible. == Applications == The hybrid argument is extensively used in cryptography. Some simple proofs using hybrid arguments are: If one cannot efficiently predict the next bit of the output of some number generator, then this generator is a pseudorandom number generator (PRG). We can securely expand a PRG with 1-bit output into a PRG with n-bit output.
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Strategic Air Command Digital Information Network

The Strategic Air Command DIgital Network (SACDIN) was a United States military computer network that provided computerized record communications, replacing the Data Transmission Subsystem and part of the Data Display Subsystem of the SAC Automated Command and Control System. SACDIN enabled a rapid flow of communications from headquarters SAC to its fielded forces, such as B-52 bases and ICBM Launch Control Centers. == Logistics == Major portions of SACDIN were developed, engineered and installed by the International Telephone and Telegraph (ITT) company, under contract to the Electronic Systems Center. == Chronology == 1969 - Headquarters SAC submits a request to the Joint Chiefs of Staff to study an expanded communications system, known as the SAC Total Information Network (SATIN). It would interconnect Air Force Satellite Communications (AFSATCOM), Advanced Airborne Command Post (AABNCP), Airborne Command Post (ABNCP), high frequency/single sideband radio HF/SSB radio, SAC Automated Command and Control System (SACCS), Automatic Digital Information Network (AUTODIN), Survivable Low Frequency Communications System (SLFCS) and Command Data Buffer (CDB) 1977 1 November - SATIN IV was effectively terminated by Congress. The restructured program was renamed SAC Digital Network (SACDIN), and was formulated to meet SAC's minimum essential data communications requirements, but also had the capability to grow in a modular fashion. 1986 ?? ??? - SACDIN replaces much of the SAC Automated Command and Control System (SACCS) and the SAC Automated Total Information Network (SATIN)
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